CN108226996B - Self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution - Google Patents

Self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution Download PDF

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CN108226996B
CN108226996B CN201711453771.6A CN201711453771A CN108226996B CN 108226996 B CN108226996 B CN 108226996B CN 201711453771 A CN201711453771 A CN 201711453771A CN 108226996 B CN108226996 B CN 108226996B
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陈辉
冯俊
陈元春
胡英
郭科
王洪辉
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    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
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Abstract

The invention discloses a self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution, which comprises the following steps of: (1)inputting two-dimensional post-stack seismic data u; (2) performing frequency domain decomposition on the two-dimensional post-stack seismic data by using the VMD to obtain IMF profiles u with different frequency rangesk(k ═ 1,2,. n), n is an integer; (3) each IMF section u after decompositionk(k ═ 1, 2.. multidot.n) is respectively processed by a self-adaptive threshold anisotropic filtering algorithm for a plurality of times of iteration processing, and a final result of reconstruction is obtained after each iteration processing
Figure DDA0001528901430000011
(4) Multiple final results obtained by multiple iterations
Figure DDA0001528901430000012
Respectively calculating the signal-to-noise ratio SNR and the similarity SSIM; (5) and selecting the optimal SNR and the final result corresponding to the SSIM for outputting. The method and the device perform denoising by combining the characteristics of the signals in the frequency domain and the time domain, better protect the local characteristics and the main structural information of the seismic data texture while filtering the noise, and simultaneously improve the quality of the seismic data.

Description

Self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution
Technical Field
The invention relates to a seismic data analysis and processing method, in particular to a self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution.
Background
The seismic data collected in the field contain useful information related to the underground structure and lithology, and the discontinuity of the underground structure and the formation edge information usually indicate the possibility of the oil and gas reservoir at the position. However, in the process of seismic data acquisition, the interference of external noise often occurs, so that the boundary and fault information is distorted or even covered, the quality of the seismic data is reduced, and the seismic data is not suitable for geological interpretation directly, so that the seismic data needs to be filtered first. In continuous research, the distribution intensity of noise in different frequency ranges is found to be different, and a traditional full-band single processing method, such as a CL model proposed by chambole and Lions, is prone to cause over-suppression of frequencies in certain frequency ranges, so that some valid information is filtered out (such as boundary, fault and the like). Therefore, the frequency division filtering has become a hot spot of current research.
The mainstream signal decomposition method at present mainly comprises Empirical Mode Decomposition (EMD), and can well perform self-adaption and multi-scale analysis on nonlinear and unstable data. However, EMD is an empirical mode decomposition method, lacks a certain mathematical theoretical basic support, and has a mode aliasing phenomenon. Both Ensemble Empirical Mode Decomposition (EEMD) and Complete Ensemble Empirical Mode Decomposition (CEEMD) improve the modal aliasing phenomenon of EMD, but both have the problem of modal redundancy and are easily interfered by strong noise when decomposing signals, so that the decomposed modes are unstable. In view of the above-mentioned problems of signal decomposition, dragomirtski and Zosso propose Variational Modal Decomposition (VMD). The VMD not only well avoids the phenomena of mode mixing and redundancy, but also has a certain inhibiting effect on high-frequency noise, and is suitable for analyzing multi-scale seismic signals.
The traditional CL model adopts a constant gradient threshold β (β is more than 0) to distinguish high and low characteristic regions, but in some complex cases, β is difficult to select, and aiming at multi-scale noise, the situation that excessive filtering is easily caused by global adoption of a gradient threshold to select, so that boundary blurring and the like are easily caused, and the interpretation of late seismic data is influenced.
Disclosure of Invention
The invention aims to provide an adaptive anisotropic frequency-division partition filtering method based on energy band distribution, which solves the problems that the threshold value of a CL model is difficult to select and the processing in the full band range is insufficient, and improves the denoising and boundary recovery capability of anisotropic filtering in a multi-scale noise environment.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: an adaptive anisotropic frequency-division partition filtering method based on energy band distribution comprises the following steps:
(1) inputting two-dimensional post-stack seismic data u;
(2) performing frequency domain decomposition on the two-dimensional post-stack seismic data by using the VMD to obtain IMF profiles u with different frequency rangesk(k ═ 1,2,. n), n is an integer and is the total number of IMF sections;
(3) each IMF section u after decompositionk(k ═ 1, 2.. multidot.n) is respectively processed by a self-adaptive threshold anisotropic filtering algorithm for a plurality of times of iteration processing, and a final result of reconstruction is obtained after each iteration processing
Figure BDA00015289014100000315
The method comprises the following specific steps:
(31) first, an adaptive threshold for the first IMF profile is calculated
Figure BDA00015289014100000316
Gradient value
Figure BDA0001528901410000031
And fidelity term εc；
(32) Dividing the gradient value according to
Figure BDA0001528901410000032
And adaptive threshold
Figure BDA00015289014100000317
By comparison, when
Figure BDA0001528901410000033
Then, adopting L2-norm filtering; when in use
Figure BDA0001528901410000034
Then, filtering by adopting a TV method to obtain a filtered IMF section
Figure BDA0001528901410000035
Figure BDA0001528901410000036
(33) Then use
Figure BDA0001528901410000037
On the basis, repeating the steps (31) and (32) for m times to obtain a filtered IMF section
Figure BDA0001528901410000038
j is the number of iterations;
(34) repeating the steps (31) to (33) to obtain corresponding IMF profiles
Figure BDA0001528901410000039
(35) The same iteration number u in each IMF sectionkjPerforming superposition reconstruction to obtain the final result after reconstruction
Figure BDA00015289014100000310
(4) Multiple final results obtained by multiple iterations
Figure BDA00015289014100000311
Respectively calculating the signal-to-noise ratio SNR and the similarity SSIM;
(5) judging the SNR and the SSIM, and selecting the optimal SNR and the final result corresponding to the SSIM
Figure BDA00015289014100000312
As a final result
Figure BDA00015289014100000313
And outputting the data.
Preferably, the method comprises the following steps: in the step (2), the VMD carries out frequency domain decomposition on the two-dimensional post-stack seismic data,
calculating u fromk(k＝1,2,...,n)
Figure BDA00015289014100000314
Where δ (t) is the dirac function, ωkRepresenting the center frequency of each band range.
Preferably, the method comprises the following steps: adaptive threshold in step (31)
Figure BDA0001528901410000041
Gradient value
Figure BDA0001528901410000042
And fidelity term εcThe calculation method of (2) is as follows:
Figure BDA0001528901410000043
Figure BDA0001528901410000044
in the formula (I), the compound is shown in the specification,
Figure BDA0001528901410000045
for the gradient operator, λ, μ, ρ ∈ (0,1), where ρ is determined by the center frequency of the IMF profile, the higher the center frequency, the larger the value of ρ.
Preferably, the method comprises the following steps: the method for calculating the signal-to-noise ratio SNR and the similarity SSIM in the step (4) comprises the following steps:
Figure BDA0001528901410000046
Figure BDA0001528901410000047
in the formula, muiIs the average intensity, δiDenotes the standard deviation, where i ∈ x, y, δxyRepresenting the covariance of the images x and y, Cj＝(KjL)2Where L is the adaptive range of pixel values, Kj1 is a constant. Typically, a small constant is selected for K.
Compared with the prior art, the invention has the advantages that: the method applies a graph denoising method to seismic data denoising, improves by combining a threshold selection problem based on a CL model to obtain an adaptive threshold anisotropic filtering method, considers local characteristics of signals in a frequency domain and a time-space domain, adjusts adaptive thresholds for different IMF sections, and distinguishes different intensity noises and characteristic attributes by combining different energy intensity ratios in different frequency bands. The method not only overcomes the problems of difficulty in selecting the CL model threshold and insufficient processing in the full frequency band range, but also improves the denoising and boundary recovery capability of anisotropic filtering in a multi-scale noise environment. The method comprises the following specific steps:
1. denoising by combining the characteristics of the signals in a frequency domain and a time domain;
2. each IMF section contains local characteristics and main structure information of the texture in the corresponding frequency range, and self-adaptive threshold value partition denoising is carried out according to the characteristics of the IMF section, so that the local characteristics and the main structure information of the texture are better protected while noise is filtered, and the quality of seismic data is improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a section of a synthetic cutting model;
FIG. 3 is a cross-sectional view of the model of FIG. 2 with the addition of random Gaussian noise;
FIG. 4 is a cross-sectional view of FIG. 3 after treatment by the method of the present invention;
FIG. 5 is a cross-sectional view of a portion of original data;
FIG. 6 is a cross-sectional view of FIG. 5 after treatment by the method of the present invention.
Detailed Description
The invention will be further explained with reference to the drawings.
Example 1: referring to fig. 1, a method for adaptive anisotropic frequency-division partition filtering based on energy band distribution includes the following steps:
(1) inputting two-dimensional post-stack seismic data u;
(2) using VMD to two-dimensional post-stack seismic dataAccording to the frequency domain decomposition, IMF profiles u with different frequency ranges are obtainedk(k ═ 1,2,. n), n is an integer; in the step (2), the VMD carries out frequency domain decomposition on the two-dimensional post-stack seismic data,
calculating u fromk(k＝1,2,...,n)
Figure BDA0001528901410000061
Where δ (t) is the dirac function, ωkRepresents the center frequency of each band range;
(3) each IMF section u after decompositionkPerforming multiple iterative processes by using an adaptive threshold anisotropic filtering algorithm, wherein a reconstructed final result u is obtained after each iterative process;
the method comprises the following specific steps:
(31) first, an adaptive threshold for the first IMF profile is calculated
Figure BDA0001528901410000062
Gradient value
Figure BDA0001528901410000063
And fidelity term εc(ii) a (ii) a Adaptive threshold in step (31)
Figure BDA0001528901410000064
Gradient value
Figure BDA0001528901410000065
And fidelity term εcThe calculation method of (2) is as follows:
Figure BDA0001528901410000066
Figure BDA0001528901410000067
in the formula (I), the compound is shown in the specification,
Figure BDA0001528901410000068
the gradient operator is lambda, mu, rho belongs to (0,1), rho is determined by the central frequency of the IMF section, and the higher the central frequency is, the larger the rho value is;
(32) dividing the gradient value according to
Figure BDA0001528901410000069
And adaptive threshold
Figure BDA00015289014100000610
By comparison, when
Figure BDA00015289014100000611
Then, adopting L2-norm filtering; when in use
Figure BDA00015289014100000612
Then, filtering by adopting a TV method to obtain a filtered IMF section
Figure BDA00015289014100000613
Figure BDA00015289014100000614
(33) Then use
Figure BDA00015289014100000615
On the basis, repeating the steps (31) and (32) for m times to obtain a filtered IMF section
Figure BDA00015289014100000616
j is the number of iterations;
(34) repeating the steps (31) to (33) to obtain corresponding IMF profiles
Figure BDA00015289014100000617
(35) The number of iterations in each IMF profile is the same
Figure BDA0001528901410000071
Performing superposition reconstruction to obtain the reconstructed final productResults
Figure BDA0001528901410000072
(4) Multiple final results obtained by multiple iterations
Figure BDA0001528901410000073
Respectively calculating the signal-to-noise ratio SNR and the similarity SSIM; the method for calculating the signal-to-noise ratio SNR and the similarity SSIM in the step (4) comprises the following steps:
Figure BDA0001528901410000074
Figure BDA0001528901410000075
in the formula, muiIs the average intensity, δiDenotes the standard deviation, where i ∈ x, y, δxyRepresenting the covariance of the images x and y, Cj＝(KjL)2Where L is the adaptive range of pixel values, Kj1 is a constant.
(5) Judging the SNR and the SSIM, and selecting the optimal SNR and the final result corresponding to the SSIM
Figure BDA0001528901410000077
As a final result
Figure BDA0001528901410000078
And outputting the data.
The method comprises the steps of inputting seismic data in the first step, and performing frequency decomposition on the two-dimensional post-stack seismic data by using the VMD in the second step, wherein the number of the optimal decomposed IMFs is determined by the data, and is generally 4-6.
Thirdly, an adaptive threshold anisotropic filtering algorithm is adopted for iterative processing, specifically, the threshold and the gradient value are utilized to divide the image, different more suitable filtering methods are selected according to different classification results, and therefore local characteristics of the texture can be better protected when noise is eliminated;
the specific method can be explained by the following demonstration:
for ease of description, a concept is introduced herein
Figure BDA0001528901410000076
n is the number of the decomposed IMF sections, and m is the number of iterations;
firstly, inputting two-dimensional post-stack seismic data u and carrying out VMD decomposition, and supposing that the IMF section u with 4 different frequency ranges is obtained by the decompositionk(k ═ 1, 2.., n), for ease of understanding we label: IMF1 ═ u1、IMF2＝u2、IMF3＝u3、IMF4＝u4；
Firstly, according to the step (31), IMF1 ═ u is calculated1Adaptive threshold of
Figure BDA00015289014100000814
Gradient value | ▽ ukI and fidelity term εc；
Then filtering is carried out according to the step (32) to obtain
Figure BDA0001528901410000081
This is the value obtained from the first filtering of the IMF1 profile.
Then use
Figure BDA0001528901410000082
And (4) repeating the steps (31) and (32) for iteration on the basis. Iterating for 19 times in sequence to obtain filtered IMF section
Figure BDA0001528901410000083
Here corresponds to the step (33)
Then, according to step (34,) obtaining
20 filtered IMF profiles of IMF2
Figure BDA0001528901410000084
20 filtered IMF profiles of IMF3
Figure BDA0001528901410000085
20 filtered IMF profiles of IMF4
Figure BDA0001528901410000086
And then, reconstructing according to the step (35) to obtain:
Figure BDA0001528901410000087
Figure BDA0001528901410000088
......
Figure BDA0001528901410000089
according to the steps (4) and (5), calculating
Figure BDA00015289014100000810
SNR and SSIM; suppose that
Figure BDA00015289014100000811
Is optimal, then
Figure BDA00015289014100000812
As a final result
Figure BDA00015289014100000813
And outputting the data.
Example 2:
an artificially synthesized two-dimensional model of the moat geology as shown in fig. 2, wherein the model contains 250 passes, each pass containing 490 sampling points and the sampling frequency is 1 ms. Two main faults are designed in the figure, and each fault comprises a breakpoint with different fault distance.
As shown in FIG. 3, FIG. 3 is a cut model section of FIG. 2 with the addition of random Gaussian noise with a signal-to-noise ratio of-1 db. Due to the influence of noise, the breakpoint of the pitch becomes fuzzy and is difficult to clearly distinguish.
FIG. 4 is a cross-sectional view of FIG. 3 after treatment by the method of the present invention; as can be seen from the upper part of FIG. 4 and the stratum, the breakpoint recovery is clear, the transverse boundary is clear, the weak amplitude is strengthened, the signal-to-noise ratio is also improved from original-1 dB to 13.4575dB, and the similarity is improved from 0.6651 to 0.9775.
Example 3:
fig. 5 and 6 show the local original actual data profile and the processed profile. As can be seen from FIG. 5, the actual data often contains different kinds of noise, and due to the existence of the noise, many weak amplitudes are covered by the noise, small intervals disappear, and the horizontal continuity of the stratum is poor, and as can be seen from the comparison between FIG. 5 and FIG. 6, the weak amplitudes covered by the noise are restored and enhanced, the intervals are clear, and the horizontal continuity of the stratum is enhanced after the processing by the method of the present invention.
The above examples are only intended to illustrate the invention, wherein the implementation steps of the method are the same as the specific implementation steps/can be changed, and all equivalent changes and modifications based on the technical scheme of the invention are not excluded from the protection scope of the invention.

Claims (2)

1. A self-adaptive anisotropic frequency division partition filtering method based on energy frequency band distribution is characterized in that: the method comprises the following steps:
(1) inputting two-dimensional post-stack seismic data u;
(2) performing frequency domain decomposition on the two-dimensional post-stack seismic data by using the VMD to obtain IMF profiles u with different frequency rangeskN, n is an integer and is the total number of IMF sections;
the VMD performs frequency domain decomposition on the two-dimensional post-stack seismic data by,
calculating u fromk，k＝1,2,...,n，
Figure FDA0002404018960000011
Where δ (t) is the dirac function, ωkRepresents the center frequency of each band range;
(3) each IMF section u after decompositionkN is processed by a self-adaptive threshold anisotropic filtering algorithm for multiple times of iteration respectively, and a final result of reconstruction is obtained after each iteration
Figure FDA0002404018960000012
The method comprises the following specific steps:
(31) first, an adaptive threshold for the first IMF profile is calculated
Figure FDA0002404018960000013
Gradient value
Figure FDA0002404018960000014
And fidelity term εcAdaptive threshold
Figure FDA0002404018960000015
Gradient value
Figure FDA0002404018960000016
And fidelity term εcThe calculation method of (2) is as follows:
Figure FDA0002404018960000017
Figure FDA0002404018960000018
in the formula (I), the compound is shown in the specification,
Figure FDA0002404018960000019
the gradient operator is lambda, mu, rho belongs to (0,1), rho is determined by the central frequency of the IMF section, and the higher the central frequency is, the larger the rho value is;
(32) dividing the gradient value according to
Figure FDA00024040189600000110
And adaptive thresholdValue of
Figure FDA00024040189600000111
By comparison, when
Figure FDA00024040189600000112
Then, adopting L2-norm filtering; when in use
Figure FDA0002404018960000021
Then, filtering by adopting a TV method to obtain a filtered IMF section
Figure FDA0002404018960000022
Figure FDA0002404018960000023
(33) Then use
Figure FDA0002404018960000024
On the basis, repeating the steps (31) and (32) for m times to obtain a filtered IMF section
Figure FDA0002404018960000025
p is the number of iterations;
(34) repeating the steps (31) to (33) to obtain corresponding IMF profiles
Figure FDA0002404018960000026
(35) The number of iterations in each IMF profile is the same
Figure FDA0002404018960000027
Performing superposition reconstruction to obtain the final result after reconstruction
Figure FDA0002404018960000028
(4) Multiple final results obtained by multiple iterations
Figure FDA0002404018960000029
Respectively calculating the signal-to-noise ratio SNR and the similarity SSIM;
(5) judging the SNR and the SSIM, and selecting the optimal SNR and the final result corresponding to the SSIM
Figure FDA00024040189600000210
As a final result
Figure FDA00024040189600000211
And outputting the data.
2. The adaptive anisotropic frequency-division multiplexing filtering method based on energy band distribution of claim 1, wherein: the method for calculating the signal-to-noise ratio SNR and the similarity SSIM in the step (4) comprises the following steps:
Figure FDA00024040189600000212
Figure FDA00024040189600000213
in the formula, muiIs the average intensity, δiDenotes the standard deviation, where i ∈ x, y, δxyRepresenting the covariance of the images x and y, Cq＝(KqL)2Q ∈ 1,2, where L is the adaptation range of the pixel value, Kq1 is a constant.
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